Non-$\pi /3(2\pi /3)$-congruent numbers and quadratic forms

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2025年10月15日

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Qianqian Cai

摘要

In this paper, by using Qin’s method (Math Ann 383(3–4):1647–1686, 2022), we give some new families of non- $\pi /3(2\pi /3$ $π / 3 (2 π / 3$ )-congruent numbers. Our results are given by some binary quadratic forms and congruence conditions modulo 16 for the 2-part of class numbers of some imaginary quadratic fields. To the author’s best knowledge, all the known results on non- $\pi /3(2\pi /3)$ $π / 3 (2 π / 3)$ -congruent numbers in the literature treated the cases when the order of the 2-primary part of the corresponding Shafarevich–Tate groups is at most 0, while our treatment improves 0 to 16.

Non-\(\pi /3(2\pi /3)\)-congruent numbers and quadratic forms

摘要